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- V. Bentkus, A. Juozulynas, V. Paulauskas, V. PAULAUSKAS
- 1999

Multidimensional stable laws G α admit a well-known Lévy–LePage series representation G α = L ∞ j=1 Γ −1/α j We present (asym-ptotically) optimal bounds for the total variation distance between a stable law and the distribution of a partial sum of the Lévy–LePage series. In the one-dimensional case similar results were obtained earlier by Bentkus, Götze and… (More)

- V Bentkus, F G Otze, V Paulauskas
- 1996

Stable laws G admit a well-known series representation of the type

In this paper we analyze Cantor type sets constructed by the removal of open intervals whose lengths are the terms of the p-sequence, {k −p } ∞ k=1. We prove that these Cantor sets are s-sets, by providing sharp estimates of their Hausdorff measure and dimension. Sets of similar structure arise when studying the set of extremal points of the boundaries of… (More)

- V Bentkus, A Juozulynas, V Paulauskas
- 1999

The standard normal distribution on R d satisses ?? @C " 6 c d ", for all " > 0 and for all convex subsets C R d , with a constant c d which depends on the dimension d only. Here @C denotes the boundary of C, and ? @C " stands for the "-neighborhood of @C. Such bounds for the normal measure of convex shells are extensively used to estimate the accuracy of… (More)

In the paper a distribution function of a sum of independent non-identically distributed bivariate random vectors is approximated by distribution function of a stable vector and the accuracy of such approximation is estimated. The obtained general result is only a little bit worse when compared with known estimates for the case of multivariate independent… (More)

- V. Paulauskas
- 2004

have given new convergence and tightness criteria for random processes whose sample paths are right-continuous and have left-limits. These criteria have been applied by Bezandry and Fernique, Bloznelis and Paulauskas to prove the central limit theorem (CLT) in the Skorohod space D[0, 1]. In this paper, using recent technique of Bezandry and Fernique, we… (More)

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